neutral balanced or not

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What do you mean by a 4-wire MWBC? Three circuits sharing one neutral on a 3? system? The neutral would carry some current unless all three loads were exactly the same. For example 3-100 watt lamps on a 4 wire MWBC fed from a 208Y/120 volt system would have 0 amps of neutral current. If one lamp burnt out the neutral current would be approximately equal to the current on the ungrounded conductors.
 
The neutral current can be calculated from the following formula, with a, B, C, and N representing the currents in the three phases and the neutral, and with "A2" meaning "A squared":

N = SQRT ( A2 + B2 + C2 -AB -AC -BC).

Try this formula with equal values of A, B, and C, and you will discover that the neutral current calculates out to zero.
 
The neutral current can be calculated from the following formula, with a, B, C, and N representing the currents in the three phases and the neutral, and with "A2" meaning "A squared":

N = SQRT ( A2 + B2 + C2 -AB -AC -BC).

Try this formula with equal values of A, B, and C, and you will discover that the neutral current calculates out to zero.
Note the result of the above formula is only accurate for loads having equal power factor.
 
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